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Pressure

🚁 Overview

Pressure is defined as the normal force applied per unit area over a surface. In static fluids, pressure acts perpendicularly to any contact boundary and is isotropic at a given depth, exerting equal magnitude in all directions.

Course Hub

Prep4Uni Fluid Mechanics 1
Serves as the main course index, organizing all foundational fluid mechanics modules and conceptual frameworks.

Chapter 2: Depth Variation

Variation of Pressure with Depth
Explores the hydrostatic equation, analyzing how fluid column weight causes linear pressure growth with depth.

Chapter 3: Measurement

Pressure Measurement
Examines industrial and laboratory tools like manometers, barometers, and Bourdon gauges for measuring pressure.

Chapter 5: Fluid Dynamics

Fluid Dynamics
Transitions from static fluids to motion analysis using velocity fields and mass conservation principles.

Chapter 6: Bernoulli Equation

Bernoulli’s Equation
Applies energy conservation along streamlines, linking fluid static pressure, dynamic head, and elevation.

📖 Contents

  1. Definition
  2. SI Unit
  3. Gauge Vs Absolute Pressure
  4. Characteristics of Pressure in Fluids
  5. Example Calculation
  6. Key Formula Recap

🎯 Learning Outcomes

  • Define pressure and express it mathematically as p = F / A, where F is the normal force and A is the area.
  • State the SI unit of pressure (pascal, Pa) and convert between Pa, kPa, bar, and atm.
  • Distinguish gauge vs. absolute pressure, and use pabs = pgauge + patm to relate them.
  • Describe the characteristics of pressure in fluids:
    • Acts perpendicular to any surface
    • Is uniform in all directions at a given depth
    • Increases with depth according to p = p0 + ρgh
  • Perform example calculations to compute pressure given force and area, and to convert between gauge and absolute pressures.
  • Recall and apply key formulas for pressure in problem-solving contexts.

1.1 Definition

Pressure (p) is defined as the force exerted normal to a unit surface area:

p = F / A

where:

  • F = normal force (N)
  • A = area over which the force acts (m2)
Pressure = F / A
Pressure = F / A

1.2 SI Unit

The SI unit of pressure is the Pascal (Pa):

1 Pa = 1 N/m2

Common derived units:

  • kilopascal: 1 kPa = 103 Pa
  • bar: 1 bar = 105 Pa
  • atmosphere: 1 atm ≈ 1.013 × 105 Pa

1.3 Gauge vs. Absolute Pressure

  • Absolute pressure (pabs): measured relative to a perfect vacuum zero reference.
  • Gauge pressure (pgauge): measured relative to local ambient atmospheric pressure.

The relationship connecting absolute and gauge pressure is:

pabs = pgauge + patm

where patm ≈ 1.013 × 105 Pa at standard sea level.

The diagram below illustrates absolute pressure when gauge pressure is measured at 50 kPa:

Gauge Pressure Versus Absolute Pressure
Gauge Pressure Versus Absolute Pressure

1.4 Characteristics of Pressure in Fluids

  • Pressure acts normal (perpendicular) to any solid surface in contact with the fluid.
Pressure acting normally on a surface
Pressure acting normally on a surface
Pressure by liquid acting normally on the surface
Pressure by liquid acting normally on the surface
  • At a given depth in a static fluid, pressure is uniform (isotropic) in all directions.
Uniform Pressure at Same Depth
Uniform Pressure at Same Depth
Pressure Increases with Depth
Pressure Increases with Depth

1.5 Example Calculations

  1. Example 1: A force of 200 N is applied uniformly to a piston of area 0.02 m2. What is the pressure?
    Solution:
    p = F / A = 200 N / 0.02 m2 = 10 000 Pa = 10 kPa
  2. Example 2: A tire gauge reads 220 kPa (gauge). What is the absolute pressure inside the tire? (Take patm = 101 kPa)
    Solution:
    pabs = pgauge + patm = 220 kPa + 101 kPa = 321 kPa

1.6 Key Formula Recap

FormulaMeaning
p = F / APressure = force per unit area
1 Pa = 1 N/m2SI unit of pressure
pabs = pgauge + patmRelation between absolute and gauge pressure

Interactive Hydrostatic Pressure & Gauge Simulator

Adjust fluid density (ρ), depth (h), and ambient atmospheric pressure (patm) to observe real-time pressure profile calculations and visual gauge response across the timeline.

Gauge Pressure: 98.10 kPa
Absolute Pressure: 199.40 kPa

Interactive Concept Toggles

Click on the concept cards below to reveal detailed explanations of fluid pressure principles.

Why does fluid pressure act perpendicular to any submerged surface?
In static fluids, shear stress is zero because fluid particles cannot sustain static shear forces without moving. Consequently, all surface contact forces must act entirely normal (perpendicular) to the surface.
What occurs when a gauge pressure reading drops below zero?
A negative gauge pressure indicates a vacuum condition where local absolute pressure is lower than ambient atmospheric pressure (pabs < patm). Absolute pressure itself cannot drop below absolute zero (0 Pa).
How does Pascal's law apply to hydraulic amplification?
Since pressure applied to a confined fluid is transmitted undiminished in all directions, applying a small input force F1 on a small piston area A1 generates an output force F2 = F1 × (A2 / A1) on a larger piston.

Frequently Asked Questions

Is pressure a scalar or vector quantity?

Pressure is a scalar quantity because at any given point in a fluid, it has magnitude but no unique directional vector—it acts equally in all directions.

Why do tire gauges read zero when unattached?

Tire gauges measure gauge pressure, which uses ambient atmospheric pressure as its reference baseline. Unattached, local pressure equals atmospheric pressure, yielding a reading of zero gauge pressure.

What standard value is assigned to 1 atmosphere (atm)?

Standard atmospheric pressure at sea level is defined as 101,325 Pa (or 101.325 kPa / 1.01325 bar / 760 mmHg).

📝 Comprehensive Practice Module

Section 1: Foundational Core Assessment

  1. What is pressure?
    Answer: Pressure is the normal force applied per unit area over a surface, expressed as p = F / A.
  2. What is the SI unit of pressure?
    Answer: The SI unit of pressure is the pascal (Pa), where 1 Pa = 1 N/m2.
  3. How many pascals are in 1 bar?
    Answer: 1 bar = 105 Pa (or 100 kPa).
  4. Define gauge pressure.
    Answer: Gauge pressure is the pressure measured relative to ambient atmospheric pressure.
  5. Define absolute pressure.
    Answer: Absolute pressure is the total pressure measured relative to a perfect vacuum reference level.
  6. State the equation relating absolute and gauge pressure.
    Answer: pabs = pgauge + patm.
  7. What typical value does atmospheric pressure have at standard sea level?
    Answer: Approximately 1.013 × 105 Pa (101.3 kPa or 1.013 bar).
  8. Is pressure a vector or scalar quantity?
    Answer: Scalar quantity.
  9. In a static fluid, does pressure vary horizontally at the same depth?
    Answer: No, pressure is uniform in all directions at a constant horizontal level in a continuous fluid.
  10. What is vacuum pressure?
    Answer: Vacuum pressure is gauge pressure below atmospheric pressure, often reported as a negative value.

Section 2: Analytical & Conceptual Analysis

  1. How does pressure change if a given force is applied over a smaller contact area?
    Answer: Pressure increases inversely with contact area because p = F / A.
  2. How does pressure change if the force doubles while the contact area remains constant?
    Answer: Pressure doubles because pressure is directly proportional to applied force.
  3. Which type of instrument directly measures absolute atmospheric pressure?
    Answer: A mercury or aneroid barometer.
  4. Which type of device measures differential or gauge pressure in closed systems?
    Answer: A Bourdon tube pressure gauge or open U-tube manometer.
  5. Why is fluid pressure in a fluid at rest isotropic?
    Answer: Fluid molecules transmit compressive forces equally in all directions because static fluids cannot sustain shear stresses without yielding.
  6. What fundamental factor causes fluid pressure to increase linearly with depth?
    Answer: The gravitational weight of the fluid column overhead acting on lower fluid layers.
  7. Why must unit systems remain dimensionally homogeneous in hydrostatic equations?
    Answer: Dimensional homogeneity ensures physical validity and prevents conversion errors across SI force (N), area (m2), and pressure (Pa) terms.
  8. If atmospheric pressure drops at high altitude, how does this impact a tire's gauge pressure reading?
    Answer: Assuming absolute tire pressure stays constant, lowering patm increases the gauge reading pgauge = pabs - patm.

Section 3: Computational & Numerical Exercises

  1. A piston of area 0.02 m2 supports a load of 500 N. Calculate the pressure exerted on the fluid.
    Solution:
    p = F / A = 500 N / 0.02 m2 = 25 000 Pa = 25 kPa.
  2. To generate a pressure of 10 kPa, over what surface area must a 200 N force act?
    Solution:
    A = F / p = 200 N / 10 000 Pa = 0.02 m2.
  3. A tire gauge reads 220 kPa (gauge). What is the absolute pressure inside the tire if atmospheric pressure is 101 kPa?
    Solution:
    pabs = pgauge + patm = 220 kPa + 101 kPa = 321 kPa.
  4. A industrial boiler pressure gauge indicates 2 bar gauge pressure. Determine its absolute pressure in pascals (take patm = 101 300 Pa).
    Solution:
    2 bar = 2 × 105 Pa = 200 000 Pa.
    pabs = 200 000 Pa + 101 300 Pa = 301 300 Pa (or 301.3 kPa).
  5. Convert 1 atm pressure into pascals and determine the height of an equivalent mercury column (ρHg = 13 600 kg/m3, g = 9.81 m/s2).
    Solution:
    1 atm = 1.013 × 105 Pa.
    h = p / (ρ × g) = 101 300 / (13 600 × 9.81) ≈ 0.760 m = 760 mmHg.
  6. A hydraulic ram has a piston surface area of 0.1 m2 operating at a gauge pressure of 3 MPa. What total normal force does it generate?
    Solution:
    F = p × A = (3 × 106 Pa) × 0.1 m2 = 3 × 105 N (300 kN).
  7. Standard atmospheric pressure acts on a flat roof measuring 2 m2. Calculate the total downward force exerted by the atmosphere (patm = 1.013 × 105 Pa).
    Solution:
    F = p × A = (1.013 × 105 Pa) × 2 m2 = 2.026 × 105 N (202.6 kN).
  8. Calculate the hydrostatic gauge pressure at a depth of 10 m in freshwater (ρ = 1000 kg/m3, g = 9.81 m/s2).
    Solution:
    pgauge = ρ × g × h = 1000 × 9.81 × 10 = 98 100 Pa = 98.1 kPa.
  9. In a mercury U-tube manometer (ρ = 13 600 kg/m3), the liquid column height difference is measured at 0.1 m. Calculate the applied gauge pressure.
    Solution:
    pgauge = ρ × g × h = 13 600 × 9.81 × 0.1 ≈ 13 341.6 Pa (13.34 kPa).
  10. A vacuum pump system reads -80 kPa gauge pressure. What is the absolute pressure inside the chamber (patm = 101 kPa)?
    Solution:
    pabs = pgauge + patm = -80 kPa + 101 kPa = 21 kPa.
Last updated: 05 Aug 2026